Shortcut: SIMPLECUBIC

Module	symfunc
Description	Usage
Calculate whether or not the coordination spheres of atoms are arranged as they would be in a simple cubic structure.
output value	type
the symmetry function for each of the specified atoms	vector

Output components

This action can calculate the values in the following table when the associated keyword is included in the input for the action. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Further details and examples

Calculate whether or not the coordination spheres of atoms are arranged as they would be in a simple cubic structure.

This shortcut is an example of a COORDINATION_SHELL_AVERAGE, which we can use to measure how similar the environment around atom $i$ is to a simple cubic structure. We perform this comparison by evaluating the following quantity:

$$s_i = \frac{ \sum_{i \ne j} \sigma(r_{ij}) \left[ \frac{ x_{ij}^4 + y_{ij}^4 + z_{ij}^4 }{r_{ij}^4} \right] }{ \sum_{i \ne j} \sigma(r_{ij}) }$$

In this expression $x_{ij}$, $y_{ij}$ and $z_{ij}$ are the $x$, $y$ and $z$ components of the vector connecting atom $i$ to atom $j$ and $r_{ij}$ is the magnitude of this vector. $\sigma(r_{ij})$ is a switching function that acts on the distance between atom $i$ and atom $j$ and its inclusion in the numerator and the denominator of the above expression as well as the fact that we are summing over all of the other atoms in the system ensures that we are calculating an average of the function of $x_{ij}$, $y_{ij}$ and $z_{ij}$ for the atoms in the first coordination sphere around atom $i$. This quantity is once again a multicolvar so you can compute it for multiple atoms using a single PLUMED action and then compute the average value for the atoms in your system, the number of atoms that have an $s_i$ value that is more that some target and so on. Notice also that you can rotate the reference frame if you are using a non-standard unit cell.

The following input tells plumed to calculate the simple cubic parameter for the atoms 1-100 with themselves. The mean value is then calculated.

Click on the labels of the actions for more information on what each action computes

SIMPLECUBICCalculate whether or not the coordination spheres of atoms are arranged as they would be in a simple cubic structure. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-100 R_0The r_0 parameter of the switching function=1.0 MEAN calculate the mean of all the quantities

The following input tells plumed to look at the ways atoms 1-100 are within 3.0 are arranged about atoms from 101-110. The number of simple cubic parameters that are greater than 0.8 is then output

Click on the labels of the actions for more information on what each action computes

SIMPLECUBICCalculate whether or not the coordination spheres of atoms are arranged as they would be in a simple cubic structure. More details SPECIESAthe list of atoms for which the symmetry function is being calculated=101-110 SPECIESBthe list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated=1-100 R_0The r_0 parameter of the switching function=3.0 MORE_THANcalculate the number of variables that are more than a certain target value. Options for this keyword are explained in the documentation for MORE_THAN.={RATIONAL R_0=0.8 NN=6 MM=12 D_0=0}

Notice that you can you can rotate the bond vectors before computing the function in the above expression as is discussed in the documentation for COORDINATION_SHELL_FUNCTION

References

More information about how this action can be used is available in the following articles: - A. D. White, G. A. Voth, Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data. Journal of Chemical Theory and Computation. 10, 3023–3030 (2014) - S. Angioletti-Uberti, M. Ceriotti, P. D. Lee, M. W. Finnis, Solid-liquid interface free energy through metadynamics simulations. Physical Review B. 81 (2010) - B. Cheng, G. A. Tribello, M. Ceriotti, Solid-liquid interfacial free energy out of equilibrium. Physical Review B. 92 (2015) - B. Cheng, G. A. Tribello, M. Ceriotti, The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit. The Journal of Chemical Physics. 147 (2017) - B. Cheng, M. Ceriotti, G. A. Tribello, Classical nucleation theory predicts the shape of the nucleus in homogeneous solidification. The Journal of Chemical Physics. 152 (2020)

Syntax

The following table describes the keywords and options that can be used with this action